Let's represent the initial amount of money each person had as follows:

Raju = R

Sam = S

Tristan = T

We know that:

R + S + T = 435

Raju spent 4/5 of his money, so he has 1/5 of his money left:

R = (1/5)R

Sam spent 2/3 of his money, so he has 1/3 of his money left:

S = (1/3)S

Tristan spent 3/4 of his money, so he has 1/4 of his money left:

T = (1/4)T

We also know that Raju has $55 more than Sam:

R = S + 55

And Tristan has $10 more than Sam:

T = S + 10

Now, we can substitute the expressions for R, S, and T into the total money equation:

(1/5)R + (1/3)S + (1/4)T = 435

Substitute R = S + 55 and T = S + 10 into the equation above:

(1/5)(S + 55) + (1/3)S + (1/4)(S + 10) = 435

Solving the equation above gives:

S = 180

Now that we have found the value of S, we can find the amount of money Tristan had at first:

T = S + 10

T = 180 + 10

T = 190

Therefore, Tristan originally had $190.